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Convergence of set-valued and fuzzy-valued martingales. (English) Zbl 0933.60041
Summary: The purpose of this paper is to prove the convergence theorems of set-valued and fuzzy-valued martingales in Kuratowski-Mosco sense without assuming that their values are compact or of compact level sets.

MSC:
60G48 Generalizations of martingales
60G99 Stochastic processes
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[1] Chatterji, S.D., Martingale convergence and the RN-theorems, Math. scand., 22, 21-41, (1968) · Zbl 0175.14503
[2] Hiai, H.; Umegaki, H., Integrals, conditional expectations and martingales of multivalued functions, J. multivariate anal., 7, 149-182, (1977) · Zbl 0368.60006
[3] Klement, E.P.; Puri, M.L.; Ralescu, D.A., Limit theorems for fuzzy random variables, (), 171-182 · Zbl 0605.60038
[4] Li, S.; Ogura, Y., Fuzzy random variables, conditional expectations and fuzzy martingales, J. fuzzy math., 4, 905-927, (1996) · Zbl 0879.60001
[5] Luu, D.Q., Representations and regularity of multivalued martingales, Acta. math. vietn., 6, 29-40, (1981) · Zbl 0522.60045
[6] Mosco, U., Convergence of convex set and of solutions of variational inequalities, Adv. math., 3, 510-585, (1969) · Zbl 0192.49101
[7] Mosco, U., On the continuity of the Young-Fenchel transform, J. math. anal. appl., 35, 518-535, (1971) · Zbl 0253.46086
[8] Papageorgiou, N.S., On the theory of Banach space valued multifunctions. 1. integration and conditional expectation, J. multivariate anal., 17, 185-206, (1985) · Zbl 0579.28009
[9] Papageorgiou, N.S., On the theory of Banach space valued multifunctions. 2. set valued martingales and set valued measures, J. multivariate anal., 17, 207-227, (1985) · Zbl 0579.28010
[10] Puri, M.L.; Ralescu, D.A., Fuzzy random variables, J. math. anal. appl., 114, 406-422, (1986) · Zbl 0605.60038
[11] Puri, M.L.; Ralescu, D.A., Convergence theorem for fuzzy martingales, J. math. anal. appl., 160, 107-121, (1991) · Zbl 0737.60005
[12] Salinetti, G.; Wets, Roger J.B., On the relations between two types of convergence for convex functions, J. math. anal. appl., 60, 211-226, (1977) · Zbl 0359.54005
[13] Salinetti, G.; Wets, Roger J.B., On the convergence of closed-valued measurable multifunctions, Trans. amer. math. soc., 226, 1, 275-289, (1981) · Zbl 0501.28005
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